Weak Orlicz spaces: Some basic properties and their applications to harmonic analysis

被引：22

作者：

Liu PeiDe ^{[1
]}

Wang MaoFa ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 04期

基金：

中国国家自然科学基金;

关键词：

weak Orlicz space; normality; maximal operator; interpolation theorem; singular integral operator; LORENTZ SPACES;

D O I：

10.1007/s11425-012-4452-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis. We first discuss the absolute continuity of the quasi-norm and its normality, then prove the boundedness of several maximal operators. We also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz spaces. As applications, the weak type analogues of several classical inequalities in harmonic analysis is obtained.

引用

页码：789 / 802

页数：14

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